[arijith]

In my bachelor thesis, I am working with a two-dimenional Navier-Stokes equation with a eddy-viscosity turbulence model for turbomachinery applications(turbine to be specific).I have a 2-d Solver only and results for that.
If turbulence is always three dimensional is there any justificattion can I forward for using a two dimensional N-S eqn with an eddy-viscosity model? Is it generally used even in conceptual design phase in industry or anywhere? though it will not properly capture the physics of the flow will it be able to capture the physics too some extent? how can I defend my postion actually?Becos I do not have time to develope a 3d model with turbulence and I have to give some justification actually.

[francesco_capuano]

Although turbulence is inherently three-dimensional, there might be cases in which the so-called mean flow is 2-D, because in the third direction turbulence is said to be 'homogeneous' (i.e., statistically invariant under translations of the reference frame). In those cases, if you solve for the mean flow variables - namely you use a RANS approach - you make no mistake in solving 2-D equations. On the other hand, if you solve for instantaneous, fluctuating variables (as in LES or DNS), then you have to solve the fully 3-D system of equations.
You said your solver uses an eddy viscosity turbulence model, so I guess it's a RANS code, is it right? In this case you don't have to worry: RANS turbulence modeling is used by the overwhelming majority of industries for design phase purposes.

[arijith]

Thanks a lot for your reply.I just want to clarify the last point - did you mean to say 2-D RANS turbulence modeling is used by the overwhelming majority of industries for design phase purposes ?
another question, is this 2-D turbulence modelling actually diffrent from 2-d Turbulence where there is no vortex streching term?

[francesco_capuano]

Originally Posted by arijith

Thanks a lot for your reply.I just want to clarify the last point - did you mean to say 2-D RANS turbulence modeling is used by the overwhelming majority of industries for design phase purposes ?

Yes, absolutely. The possibility to use 2D grids is one of the major advantages of the RANS approach.

Originally Posted by arijith

another question, is this 2-D turbulence modelling actually diffrent from 2-d Turbulence where there is no vortex streching term?

I'm not sure I have fully understood your question. What do you mean by 2-d turbulence where there is no vortex stretching term? Strictly speaking, turbulence is always three-dimensional - in fact, the vortex stretching term appears only in 3D equations, the correspondent mechanism being fundamental in the turbulent energy cascade process. As far as I know, it does have a sense to speak about '2D turbulence' only for very large-scale motions (e.g. atmosphere and oceans).

[sbaffini]

The 2D approach Francesco is referring to has nothing in common with 2D turbulence (except the 2D concept itself).

2D turbulence is a mathematical concept related to the 2D instantaneous Navier-Stokes equations. These equations exhibit a chaotic non-linear behaviour also known as 2D turbulence; obviously, a very strong difference in this theoretical system (with respect to reality) comes from the fact that the vortex stretching term is missing. In practice, in 2D, a lot of degrees of freedom and energy modes are missing so the system obviously evolves differently. Still, very large scale phenomena in the atmosphere have a lot of similarities with this 2D system, due to the very different sizes of the horizontal and vertical length scales usually involved.

The possibility of using a 2D RANS approach comes instead from the 3D Navier-Stokes equations when Reynolds averaged. I don't know if there is any sound proof for this but, the general idea is that if the boundary conditions (intended in the most general sense) have symmetries then these are also shared by the time averaged flow field, laminar or turbulent.

So yes, 2D RANS is fully applicable; actually, it is a feasible choice every time the 3D effects can be assumed to be negligible. Nonetheless, this tells you a lot about the tremendous task the RANS models have to face (2D, 3D, someone also asks for unsteadiness in 2D/3D... it is really a lot)

Of course this is just part of the story as i'm pretty sure there are some specific cases where, even with symmetric boundary conditions, a stable symmetric flow field can't be achieved (or, put differently, the symmetric solution is not stable). This is true for the real flow situations, the 3D mathematical model we call N.S. equations and sometimes also for the 2D version of the model. However, once you put an eddy viscosity model in your equations everything changes

[FMDenaro]

Originally Posted by sbaffini

The 2D approach Francesco is referring to has nothing in common with 2D turbulence (except the 2D concept itself).

2D turbulence is a mathematical concept related to the 2D instantaneous Navier-Stokes equations. These equations exhibit a chaotic non-linear behaviour also known as 2D turbulence; obviously, a very strong difference in this theoretical system (with respect to reality) comes from the fact that the vortex stretching term is missing. In practice, in 2D, a lot of degrees of freedom and energy modes are missing so the system obviously evolves differently. Still, very large scale phenomena in the atmosphere have a lot of similarities with this 2D system, due to the very different sizes of the horizontal and vertical length scales usually involved.

The possibility of using a 2D RANS approach comes instead from the 3D Navier-Stokes equations when Reynolds averaged. I don't know if there is any sound proof for this but, the general idea is that if the boundary conditions (intended in the most general sense) have symmetries then these are also shared by the time averaged flow field, laminar or turbulent.

So yes, 2D RANS is fully applicable; actually, it is a feasible choice every time the 3D effects can be assumed to be negligible. Nonetheless, this tells you a lot about the tremendous task the RANS models have to face (2D, 3D, someone also asks for unsteadiness in 2D/3D... it is really a lot)

Of course this is just part of the story as i'm pretty sure there are some specific cases where, even with symmetric boundary conditions, a stable symmetric flow field can't be achieved (or, put differently, the symmetric solution is not stable). This is true for the real flow situations, the 3D mathematical model we call N.S. equations and sometimes also for the 2D version of the model. However, once you put an eddy viscosity model in your equations everything changes

I agree, the concept of the 2D RANS implies the use of a statistical average on the 3D NS equations and the hypotesis that the flow is statistically 2D.

[arijith]

Thanks a lot for your reply.